The interior regularity results of Seregin, Silvestre, Šverák, and Zlatoš lead naturally to questions about
boundary regularity. In [1]}, the second and the fourth authors studied the boundary behavior of weak solutions.
It turns out that many results for elliptic operators with bounded, measurable coefficients can be extended to this setting. For example, they proved the boundary Hölder regularity of the solution, established the existence of the elliptic measure \(\omega \)  associated to these operators, and offered multiple characterizations of the mutual absolute continuity of the elliptic measure and the surface measure in Lipschitz domains. This work laid out the background necessary to
launch the investigation into boundary value problems for elliptic operators having a \(\operatorname{BMO}\)  anti-symmetric part.
